Time-Ordered Product Expansions for Computational Stochastic Systems Biology

TL;DR

This paper introduces a novel framework using time-ordered product expansions from quantum field theory to derive and interpret algorithms for stochastic biochemical networks, including Gillespie's SSA and hybrid models.

Contribution

It applies the time-ordered product framework to systematically derive simulation and parameter-learning algorithms for complex stochastic biochemical systems.

Findings

Derived Gillespie's SSA using Feynman diagrams

Developed new algorithms for stochastic reaction networks

Extended to hybrid stochastic differential equation models

Abstract

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's Stochastic Simulation Algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion (TOPE) can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems.